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Low-Rank Adaptation (LoRA) is a widely adopted method for customizing large-scale language models. In distributed, untrusted training environments, an open source base model user may want to use LoRA weights created by an external contributor, leading to two requirements: (1) the base model user must confirm that the LoRA weights are effective when paired with the intended base model, and (2) the LoRA contributor must keep their proprietary weights private until compensation is assured. We present ZKLoRA, a zero-knowledge verification protocol that relies on succinct proofs and our novel Multi-Party Inference procedure to verify LoRA-base model compatibility without exposing LoRA weights. ZKLoRA produces deterministic correctness guarantees and validates each LoRA module in only 1-2 seconds on state-of-the-art large language models. This low-latency approach enables nearly real-time verification and promotes secure collaboration among geographically decentralized teams and contract-based training pipelines. The protocol ensures that the delivered LoRA module works as claimed, safeguarding the contributor's intellectual property while providing the base model user with verification of compatibility and lineage., Comment: 7 pages, 3 figures

We present the most extensive set to date of high-quality RR Lyrae light curve templates in the griz bands, based on time-series observations of the Dark Energy Camera Plane Survey (DECaPS) East field, located in the Galactic bulge at coordinates (RA, DEC)(J2000) = (18:03:34, -29:32:02), obtained with the Dark Energy Camera (DECam) on the 4-m Blanco telescope at the Cerro Tololo Inter-American Observatory (CTIO). Our templates, which cover both fundamental-mode (RRab) and first-overtone (RRc) pulsators, can be especially useful when there is insufficient data for accurately calculating the average magnitudes and colors, hence distances, as well as to inform multi-band light curve classifiers, as will be required in the case of the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST). In this paper, we describe in detail the procedures that were adopted in producing these templates, including a novel approach to account for the presence of outliers in photometry. Our final sample comprises 136 RRab and 144 RRc templates, all of which are publicly available. Lastly, in this paper we study the inferred Fourier parameters and other light curve descriptors, including rise time,skewness, and kurtosis, as well as their correlations with the pulsation mode, period, and effective wavelength., Comment: 19 pages, 17 figures and 4 tables

Model-Free Control (MFC) has been applied to a wide variety of systems in which it has shown its performance. MFC offers "model-free operation", but the controller design requires some information from the nominal plant. This paper introduces a new design method for model-free controllers that uses minimal data about the system and retrieves a set of stable controller configurations. This method is specifically developed for first-order model-free controllers, but can be extended to second-order controllers, and it relies in a frequency analysis of the controller and the plant. The main feature of the design method is decoupling the design of the main control parameter alpha from the rest, providing specific values for it. The efficacy of the proposed method will be showcased with some relevant application examples., Comment: Conference paper, 7 pages

We measure the growth of cosmic density fluctuations on large scales and across the redshift range $0.3

We present a joint analysis of the CMB lensing power spectra measured from the Data Release 6 of the Atacama Cosmology Telescope and Planck PR4, cross-correlations between the ACT and Planck lensing reconstruction and galaxy clustering from unWISE, and the unWISE clustering auto-spectrum. We obtain 1.5% constraints on the matter density fluctuations at late times parametrised by the best constrained parameter combination $S_8^{\rm 3x2pt}\equiv\sigma_8 (\Omega_m/0.3)^{0.4}=0.815\pm0.012$. The commonly used $S_8\equiv\sigma_8 (\Omega_m/0.3)^{0.5}$ parameter is constrained to $S_8=0.816\pm0.015$. In combination with baryon acoustic oscillation (BAO) measurements we find $\sigma_8=0.815\pm 0.012$. We also present sound-horizon-independent estimates of the present day Hubble rate of $H_0=66.4^{+3.2}_{-3.7} \,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$ from our large scale structure data alone and $H_0=64.3^{+2.1}_{-2.4}\,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$ in combination with uncalibrated supernovae from Pantheon+. Using parametric estimates of the evolution of matter density fluctuations, we place constraints on cosmic structure in a range of high redshifts typically inaccessible with cross-correlation analyses. Combining lensing cross- and auto-correlations, we derive a 3.3% constraint on the integrated matter density fluctuations above $z=2.4$, one of the tightest constraints in this redshift range and fully consistent with a $\Lambda$CDM model fit to the primary CMB from Planck. Combining with primary CMB observations and using the extended low redshift coverage of these combined data sets we derive constraints on a variety of extensions to the $\Lambda$CDM model including massive neutrinos, spatial curvature, and dark energy. We find in flat $\Lambda$CDM $\sum m_\nu<0.12$ eV at 95% confidence using the LSS data, BAO measurements from SDSS and primary CMB observations., Comment: 30 pages, 15 figures, accepted for publication in PRD, data available under https://portal.nersc.gov/project/act/act_x_unWISE_xcorr+3x2pt/

We infer the growth of large scale structure over the redshift range $0.4\lesssim z \lesssim 1$ from the cross-correlation of spectroscopically calibrated Luminous Red Galaxies (LRGs) selected from the Dark Energy Spectroscopic Instrument (DESI) legacy imaging survey with CMB lensing maps reconstructed from the latest Planck and ACT data. We adopt a hybrid effective field theory (HEFT) model that robustly regulates the cosmological information obtainable from smaller scales, such that our cosmological constraints are reliably derived from the (predominantly) linear regime. We perform an extensive set of bandpower- and parameter-level systematics checks to ensure the robustness of our results and to characterize the uniformity of the LRG sample. We demonstrate that our results are stable to a wide range of modeling assumptions, finding excellent agreement with a linear theory analysis performed on a restricted range of scales. From a tomographic analysis of the four LRG photometric redshift bins we find that the rate of structure growth is consistent with $\Lambda$CDM with an overall amplitude that is $\simeq5-7\%$ lower than predicted by primary CMB measurements with modest $(\sim2\sigma)$ statistical significance. From the combined analysis of all four bins and their cross-correlations with Planck we obtain $S_8 = 0.765\pm0.023$, which is less discrepant with primary CMB measurements than previous DESI LRG cross Planck CMB lensing results. From the cross-correlation with ACT we obtain $S_8 = 0.790^{+0.024}_{-0.027}$, while when jointly analyzing Planck and ACT we find $S_8 = 0.775^{+0.019}_{-0.022}$ from our data alone and $\sigma_8 = 0.772^{+0.020}_{-0.023}$ with the addition of BAO data. These constraints are consistent with the latest Planck primary CMB analyses at the $\simeq 1.6-2.2\sigma$ level, and are in excellent agreement with galaxy lensing surveys., Comment: 60 pages, 26 figures, comments welcome

We present a high-significance cross-correlation of CMB lensing maps from the Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) with spectroscopically calibrated luminous red galaxies (LRGs) from the Dark Energy Spectroscopic Instrument (DESI). We detect this cross-correlation at a significance of 38$\sigma$; combining our measurement with the Planck Public Release 4 (PR4) lensing map, we detect the cross-correlation at 50$\sigma$. Fitting this jointly with the galaxy auto-correlation power spectrum to break the galaxy bias degeneracy with $\sigma_8$, we perform a tomographic analysis in four LRG redshift bins spanning $0.4 \le z \le 1.0$ to constrain the amplitude of matter density fluctuations through the parameter combination $S_8^\times = \sigma_8 \left(\Omega_m / 0.3\right)^{0.4}$. Prior to unblinding, we confirm with extragalactic simulations that foreground biases are negligible and carry out a comprehensive suite of null and consistency tests. Using a hybrid effective field theory (HEFT) model that allows scales as small as $k_{\rm max}=0.6$ $h/{\rm Mpc}$, we obtain a 3.3% constraint on $S_8^\times = \sigma_8 \left(\Omega_m / 0.3\right)^{0.4} = 0.792^{+0.024}_{-0.028}$ from ACT data, as well as constraints on $S_8^\times(z)$ that probe structure formation over cosmic time. Our result is consistent with the early-universe extrapolation from primary CMB anisotropies measured by Planck PR4 within 1.2$\sigma$. Jointly fitting ACT and Planck lensing cross-correlations we obtain a 2.7% constraint of $S_8^\times = 0.776^{+0.019}_{-0.021}$, which is consistent with the Planck early-universe extrapolation within 2.1$\sigma$, with the lowest redshift bin showing the largest difference in mean. The latter may motivate further CMB lensing tomography analyses at $z<0.6$ to assess the impact of potential systematics or the consistency of the $\Lambda$CDM model over cosmic time., Comment: Prepared for submission to JCAP (47 pages, 13 figures)

Occupancy Grids have been widely used for perception of the environment as they allow to model the obstacles in the scene, as well as free and unknown space. Recently, there has been a growing interest in the unknown space due to the necessity of better understanding the situation. Although Occupancy Grids have received numerous extensions over the years to address emerging needs, currently, few works go beyond the delimitation of the unknown space area and seek to incorporate additional information. This work builds upon the already well-established LiDAR-based Dynamic Occupancy Grid to introduce a complementary Categorized Grid that conveys its estimation using semantic labels while adding new insights into the possible causes of unknown space. The proposed categorization first divides the space by occupancy and then further categorizes the occupied and unknown space. Occupied space is labeled based on its dynamic state and reliability, while the unknown space is labeled according to its possible causes, whether they stem from the perception system's inherent constraints, limitations induced by the environment, or other causes. The proposed Categorized Grid is showcased in real-world scenarios demonstrating its usefulness for better situation understanding., Comment: Submitted to the 27th IEEE International Conference on Intelligent Transportation Systems

Motion prediction is a key factor towards the full deployment of autonomous vehicles. It is fundamental in order to ensure safety while navigating through highly interactive and complex scenarios. Lack of visibility due to an obstructed view or sensor range poses a great safety issue for autonomous vehicles. The inclusion of occlusion in interaction-aware approaches is not very well explored in the literature. In this work, the MultIAMP framework, which produces multimodal probabilistic outputs from the integration of a Dynamic Bayesian Network and Markov chains, is extended to tackle occlusions. The framework is evaluated with a state-of-the-art motion planner in two realistic use cases.

In this paper we study equation $$(x-dr)^5+\cdots+x^5+\cdots+(x+dr)^5=y^p$$ under the condition $\gcd(x,r)=1$. We present a recipe for proving the non-existence of non-trivial integer solutions of the above equation, and as an application we obtain explicit results for the cases $d=2,3$ (the case $d=1$ was already solved). We also prove an asymptotic result for $d\equiv 1, 7\pmod9$. Our main tools include the modular method, employing Frey curves and their associated modular forms, as well as the symplectic argument., Comment: Comments welcome

We present a linear cutting-plane relaxation approach that rapidly proves tight lower bounds for the Alternating Current Optimal Power Flow Problem (ACOPF). Our method leverages outer-envelope linear cuts for well-known second-order cone relaxations for ACOPF along with modern cut management techniques. These techniques prove effective on a broad family of ACOPF instances, including the largest ones publicly available, quickly and robustly yielding sharp bounds. Our primary focus concerns the (frequent) case where an ACOPF instance is considered following a small or moderate change in problem data, e.g., load changes and generator or branch shut-offs. We provide significant computational evidence that the cuts computed on the prior instance provide an effective warm-start for our algorithm., Comment: arXiv admin note: substantial text overlap with arXiv:2312.04251

We present a pure linear cutting-plane relaxation approach for rapidly proving tight and accurate lower bounds for the Alternating Current Optimal Power Flow Problem (ACOPF) and its multi-period extension with ramping constraints. Our method leverages outer-envelope linear cuts for well-known second-order cone relaxations for ACOPF together with modern cut management techniques and reformulations to attain numerical stability. These techniques prove effective on a broad family of ACOPF instances, including the largest ones publicly available, quickly and robustly yielding tight bounds. Additionally, we consider the (frequent) case where an ACOPF instance is handled following a small or moderate change in problem data, e.g., load changes and generator or branch shut-offs. We provide significant computational evidence, on single and multi-period ACOPF instances, that the cuts computed on the prior instance provide very good lower bounds when warm-starting our algorithm on the perturbed instance.

The selection of an appropriate control strategy is essential for ensuring safe operation in autonomous driving. While numerous control strategies have been developed for specific driving scenarios, a comprehensive comparative assessment of their performance using the same tuning methodology is lacking in the literature. This paper addresses this gap by presenting a systematic evaluation of state-of-the-art model-free and model-based control strategies. The objective is to evaluate and contrast the performance of these controllers across a wide range of driving scenarios, reflecting the diverse needs of autonomous vehicles. To facilitate the comparative analysis, a comprehensive set of performance metrics is selected, encompassing accuracy, robustness, and comfort. The contributions of this research include the design of a systematic tuning methodology, the use of two novel metrics for stability and comfort comparisons and the evaluation through extensive simulations and real tests in an experimental instrumented vehicle over a wide range of trajectories., Comment: Video showcasing a real-world test of a model-free lateral controller in an automated vehicle: https://youtu.be/JtLfZzEdGC8

Recent advancements in natural language processing by large language models (LLMs), such as GPT-4, have been suggested to approach Artificial General Intelligence. And yet, it is still under dispute whether LLMs possess similar reasoning abilities to humans. This study evaluates GPT-4 and various other LLMs in judging the profoundness of mundane, motivational, and pseudo-profound statements. We found a significant statement-to-statement correlation between the LLMs and humans, irrespective of the type of statements and the prompting technique used. However, LLMs systematically overestimate the profoundness of nonsensical statements, with the exception of Tk-instruct, which uniquely underestimates the profoundness of statements. Only few-shot learning prompts, as opposed to chain-of-thought prompting, draw LLMs ratings closer to humans. Furthermore, this work provides insights into the potential biases induced by Reinforcement Learning from Human Feedback (RLHF), inducing an increase in the bias to overestimate the profoundness of statements., Comment: 5 pages, 3 figures

Motion prediction is a key factor towards the full deployment of autonomous vehicles. It is fundamental in order to assure safety while navigating through highly interactive complex scenarios. In this work, the framework IAMP (Interaction- Aware Motion Prediction), producing multi-modal probabilistic outputs from the integration of a Dynamic Bayesian Network and Markov Chains, is extended with a learning-based approach. The integration of a machine learning model tackles the limitations of the ruled-based mechanism since it can better adapt to different driving styles and driving situations. The method here introduced generates context-dependent acceleration distributions used in a Markov-chain-based motion prediction. This hybrid approach results in better evaluation metrics when compared with the baseline in the four, Comment: Accepted for publication at the IEEE Intelligent Vehicle Symposium 2023

Model-Free Control has proven its performance in a wide variety of systems. Although its adequate tuning can be achieved using the knowledge of the system and optimization-based approaches, there is not yet a systematic design procedure for this kind of control scheme. In this paper, a non-iterative Three Term Controller tuning procedure is adapted and extended to fit Model-free controllers' structure. This procedure is successfully applied to design the lateral control of an automated car with realistic performance requirements., Comment: submitted to IFAC World Congress 2023

Let $f$ and $g$ be two different newforms without complex multiplication having the same coefficient field. The main result of the present article proves that a congruence between the Galois representations attached to $f$ and to $g$ for a large prime $p$ implies an isomorphism between the endomorphism algebras of the abelian varieties $A_f$ and $A_g$ attached to $f$ and $g$ by the Eichler-Shimura construction. This implies important relations between their building blocks. A non-trivial application of our result is that for all prime numbers $d$ congruent to $3$ modulo $8$ satisfying that the class number of $\mathbb{Q}(\sqrt{-d})$ is prime to $3$, the equation $x^4+dy^2 =z^p$ has no non-trivial primitive solutions when $p$ is large enough. We prove a similar result for the equation $x^2+dy^6=z^p$., Comment: 20 pages

This paper presents a new optical imaging survey of four deep drilling fields (DDFs), two Galactic and two extragalactic, with the Dark Energy Camera (DECam) on the 4 meter Blanco telescope at the Cerro Tololo Inter-American Observatory (CTIO). During the first year of observations in 2021, $>$4000 images covering 21 square degrees (7 DECam pointings), with $\sim$40 epochs (nights) per field and 5 to 6 images per night per filter in $g$, $r$, $i$, and/or $z$, have become publicly available (the proprietary period for this program is waived). We describe the real-time difference-image pipeline and how alerts are distributed to brokers via the same distribution system as the Zwicky Transient Facility (ZTF). In this paper, we focus on the two extragalactic deep fields (COSMOS and ELAIS-S1), characterizing the detected sources and demonstrating that the survey design is effective for probing the discovery space of faint and fast variable and transient sources. We describe and make publicly available 4413 calibrated light curves based on difference-image detection photometry of transients and variables in the extragalactic fields. We also present preliminary scientific analysis regarding Solar System small bodies, stellar flares and variables, Galactic anomaly detection, fast-rising transients and variables, supernovae, and active galactic nuclei., Comment: 22 pages, 17 figures, 2 tables. Accepted to MNRAS

In order to increase the number of situations in which an intelligent vehicle can operate without human intervention, lateral control is required to accurately guide it in a reference trajectory regardless of the shape of the road or the longitudinal speed. Some studies address this problem by tuning a controller for low and high speeds and including an output adaptation law. In this paper, a strategy framed in the Model-Free Control paradigm is presented to laterally control the vehicle over a wide speed range. Tracking quality, system stability and passenger comfort are thoroughly analyzed and compared to similar control structures. The results obtained both in simulation and with a real vehicle show that the developed strategy tracks a large number of trajectories with high degree of accuracy, safety and comfort., Comment: 8th Joint IFAC Conference: SSSC-TDS-LPV, September 27-30, 2022 -- Montreal, Canada

Let $K$ be a number field. Using the modular method, we prove asymptotic results on solutions of the Diophantine equation $x^4-y^2=z^p$ over $K$, assuming some deep but standard conjectures of the Langlands programme when $K$ has at least one complex embedding. On the other hand, we give unconditional results in the case of totally real extensions having odd narrow class number and a unique prime above $2$. When modularity of elliptic curves over $K$ is known, for example when $K$ is real quadratic or the $r$-layer of the cyclotomic $\mathbb{Z}_2$-extension of $\mathbb{Q}$, effective asymptotic results hold., Comment: 9 pages. Comments are welcome!

Since the cyberspace consolidated as fifth warfare dimension, the different actors of the defense sector began an arms race toward achieving cyber superiority, on which research, academic and industrial stakeholders contribute from a dual vision, mostly linked to a large and heterogeneous heritage of developments and adoption of civilian cybersecurity capabilities. In this context, augmenting the conscious of the context and warfare environment, risks and impacts of cyber threats on kinetic actuations became a critical rule-changer that military decision-makers are considering. A major challenge on acquiring mission-centric Cyber Situational Awareness (CSA) is the dynamic inference and assessment of the vertical propagations from situations that occurred at the mission supportive Information and Communications Technologies (ICT), up to their relevance at military tactical, operational and strategical views. In order to contribute on acquiring CSA, this paper addresses a major gap in the cyber defence state-of-the-art: the dynamic identification of Key Cyber Terrains (KCT) on a mission-centric context. Accordingly, the proposed KCT identification approach explores the dependency degrees among tasks and assets defined by commanders as part of the assessment criteria. These are correlated with the discoveries on the operational network and the asset vulnerabilities identified thorough the supported mission development. The proposal is presented as a reference model that reveals key aspects for mission-centric KCT analysis and supports its enforcement and further enforcement by including an illustrative application case., Comment: Preprint of an extended version of the conference "A novel automatic discovery system of critical assets in cyberspace-oriented military missions", in Proc. of the First Workshop on Recent Advances in Cyber Situational Awareness on Military Operations (CSA 2020) held by the 15th ARES International Conference in August 2020. https://doi.org/10.1145/3407023.3409225